Determine whether the given function is linear. If the function is linear, express the function in the form f(x) = ax + b. (If the function is not linear, enter NOT LINEAR.) f(x) = x(2 - x) f(x) =
Determine whether the given function is linear. If the function is linear, express the function in the form f(x) = ax + b. (If the function is not linear, enter NOT LINEAR.) f(x) = x(2 - x) f(x) =
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Determining Whether a Function is Linear**
**Objective:**
Determine whether the given function is linear. If the function is linear, express the function in the form \( f(x) = ax + b \). (If the function is not linear, enter NOT LINEAR.)
**Task:**
Given function:
\[ f(x) = x (2 - x) \]
**Interactive Element:**
A text box is provided for the user to input the form of the function if it is linear or to state "NOT LINEAR" if it is not.
**Instructions:**
1. Simplify the function if possible.
2. Check if the function can be represented in the form \( f(x) = ax + b \).
3. If the result matches this form, input the linear expression.
4. If the function does not match the form \( f(x) = ax + b \), input "NOT LINEAR" in the provided box.
**Example:**
1. Simplify the function:
\[ f(x) = x(2 - x) = 2x - x^2 \]
2. Identify the form:
\[ 2x - x^2 \]
3. Since the function includes a quadratic term (\( x^2 \)), it cannot be expressed in the linear form \( f(x) = ax + b \).
4. Therefore, input "NOT LINEAR" in the text box.
Insert your response here:
\[ f(x) = \boxed{\phantom{a}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F26522578-6957-488e-b440-649df0842474%2Fc011094a-9504-49ba-aad7-1331a5f4c8bb%2Fo5qplaa_processed.png&w=3840&q=75)
Transcribed Image Text:**Determining Whether a Function is Linear**
**Objective:**
Determine whether the given function is linear. If the function is linear, express the function in the form \( f(x) = ax + b \). (If the function is not linear, enter NOT LINEAR.)
**Task:**
Given function:
\[ f(x) = x (2 - x) \]
**Interactive Element:**
A text box is provided for the user to input the form of the function if it is linear or to state "NOT LINEAR" if it is not.
**Instructions:**
1. Simplify the function if possible.
2. Check if the function can be represented in the form \( f(x) = ax + b \).
3. If the result matches this form, input the linear expression.
4. If the function does not match the form \( f(x) = ax + b \), input "NOT LINEAR" in the provided box.
**Example:**
1. Simplify the function:
\[ f(x) = x(2 - x) = 2x - x^2 \]
2. Identify the form:
\[ 2x - x^2 \]
3. Since the function includes a quadratic term (\( x^2 \)), it cannot be expressed in the linear form \( f(x) = ax + b \).
4. Therefore, input "NOT LINEAR" in the text box.
Insert your response here:
\[ f(x) = \boxed{\phantom{a}} \]
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